糖心Vlog

Laura DeMarco

Hollis Professor of Mathematicks and Natural
Philosophy at Harvard University

October 13-15, 2026

The lecture on Tuesday is intended for all those interested in mathematics. The remaining lectures are intended for a more mathematically experienced audience.

Refreshments will be served 30 minutes before each lecture

Abstract:听One of the most famous (and still not fully understood) objects in mathematics is the Mandelbrot set. By definition, it is the set of complex numbers c for which the recursive sequence defined by x_1 = c and x_{n+1} = (x_n)^2+c is bounded. This set turns out to be rich and complicated and related to many different areas of mathematics. In the first talk, I will present an overview of what's known and what's not known about the Mandelbrot set, and I'll describe recent work that (perhaps surprisingly) employs tools from number theory and arithmetic geometry. In the second talk, I will explain historical connections to the study of elliptic curves and the geometry of their torsion points, and I will show how our analysis of bifurcations (for example, in studying the Mandelbrot set) allowed us to say new things. I will present a broader conjecture on the geometry of periodic points for dynamical systems on projective varieties, encompassing many well-known results from the last 50 years. The third talk is focused on my recent work with Myrto Mavraki on algebraic relations that can arise between distinct maps on P^1 and among their periodic points.